Zhiyun Kuang © May, 2004

Adaptive Notch Filter

Application on modifying signal without changing frequency domain.

Zhiyun Kuang © May, 2004

Copyright of Sound bank

• $10,000 spent to record one piano sound bank.• Easy to make illegal copy.• Want to make characteristic on the signal

without corrupting it.

Zhiyun Kuang © May, 2004

Sound properties

• Sound: A x Sin(2πω+Ө)

• A => Magnitude => Loudness• ω => Frequency => Pitch, Location• Ө => Phase => reverb, echo, loudness

Zhiyun Kuang © May, 2004

Time domain vs Frequency domain

Zhiyun Kuang © May, 2004

Zhiyun Kuang © May, 2004

Two problems:

1. Avoid canceling other frequency

2. Track original signal

Zhiyun Kuang © May, 2004

Least Mean Square algorithm

Zhiyun Kuang © May, 2004

Matlab Codex1 = C*cos(2*pi*w0*t);x2 = C*sin(2*pi*w0*t);

x3 = C*cos(2*pi*w0*t+theta);x4 = C*sin(2*pi*w0*t+theta);

for i = L:length(T) temp_x1 = x1(i:-1:i-L+1); temp_x2 = x2(i:-1:i-L+1); temp_x3 = x3(i:-1:i-L+1); temp_x4 = x4(i:-1:i-L+1);

yk1 = sum(w1.*temp_x1); yk2 = sum(w2.*temp_x2); yk3 = sum(w1.*temp_x3); yk4 = sum(w2.*temp_x4);

y(i) = yk1+yk2; yref(i) = (yk3+yk4); e = d(i)-y(i); for j=(1:L) w1(j)=w1(j)+2*u*e*temp_x1(j); w2(j)=w2(j)+2*u*e*temp_x2(j); endend

Zhiyun Kuang © May, 2004

Zhiyun Kuang © May, 2004

Zhiyun Kuang © May, 2004

Zhiyun Kuang © May, 2004

Zhiyun Kuang © May, 2004

Conclusion

• Can use notch filter to filter certain frequency, but hard to improve accuracy and track the represent signal.

• Adaptive notch filter can easily control the width of the filter and track the represent signal.

• Using the relationship of the C, μ, ө, can change a signal to have some characteristic, without changing its frequency domain.